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The means and mean absolute deviations of the individual times of members of two relay swim teams are shown in the table below.
Means and Mean Absolute Deviations of
Individual Times of Members of 4*200- meter Relay Swim Teams

Team A Team B
Mean 127.9 s 127.4 s
Mean Absolute Deviation 0.26 s 0.23 s
The difference of the means is found and then compared to each of the mean absolute deviations. Which is true?
The difference between the mean times is about equal to the mean absolute deviation of the data sets.
The difference between the mean times is about 2 times the mean absolute deviation of the data sets.
The difference between the mean times is about 5 times the mean absolute deviation of the data sets.
The difference between the mean times is about 16 times the mean absolute deviation of the data sets.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

127.9-127.4=0.5
0.26-0.23=0.03
0.5/0.03=16.6666

About 16 times

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virtuematane virtuematane · Answer 2 · 2019-05-03T11:07:00+02:00

Answer:

The difference between the mean times is about 16 times the mean absolute deviation of the data sets.

Step-by-step explanation:

We are given the mean and mean absolute deviation of two teams in a table as:

Team A Team B

Mean 127.9 s 127.4 s

Mean Absolute Deviation 0.26 s 0.23 s

The difference of mean between two team is: 0.5 s

( Since 127.9-127.4=0.5 s)

Also, the difference of Mean absolute deviation is: 0.03 s

( Since, 0.26-0.23=0.03 s)

Now let the difference of the mean times be equal t n times the difference of the mean absolute deviation of two teams

i.e.

0.5=n×0.03

⇒ n=0.5/0.03

⇒ n=16.6667

which is approximately equal to 16.

Hence, The difference between the mean times is about 16 times the mean absolute deviation of the data sets.